Ordinal Arithmetic

Abstract

In Section 7 we defined α + 1 to be α ∪ {α}. We proved that α + 1 is an ordinal, that is, α + 1 is a transitive set that is well ordered by the ∈-relation. As a well ordered set α + 1 has an initial segment α and its “terminal” segment beginning with α consists of just a single element, namely α.